Timekeeping measurements always rely on the comparison of two oscillators; when you check to see if your clock or watch is running fast or slow, you do this by comparing it to another clock. Finding disagreement between two clocks won’t tell you *a priori* which one is the culprit, just as in the adage that a man with two clocks is never sure what time it is. But comparing three clocks allow pair-wise comparisons, and begin to allow one to assign a stability to the individual clocks.

Comparisons are what the scientists did in the second paper in my review, “Time, Analysis of records made on the Loomis chronograph by three Shortt clocks and a crystal oscillator.” The quartz crystal oscillator gave the input to the Loomis chronograph, and the three Shortt clocks were compared to crystal, and could then be compared with each other by differencing the data, which removes the crystal from the measurement.

The interesting (to me) part of the paper begins a few pages in, where they begin discussing the influence of the moon. The moon should give rise to a change in amplitude that would occur over an interval of 24h 50m, and should be distinguishable from diurnal terms present in the pendulum clocks. Two different time series were analyzed, one having a duration of 54 days, and the other having a duration of 146 days. This was long enough to average out noise terms, since the preliminary estimate of the effect was 153 microseconds per half-period of oscillation (i.e. one second)

The theory of the effect of direct attraction is presented in terms of tidal potentials, and it, of course, ends up depending on the angular position of the moon and the latitude of the observer. There are secondary effects as well. The tidal effect of the moon is not only on the water, but on the solid earth as well, though because it is not particularly elastic, the earth’s deflection is smaller, and this changes the radius by a small amount. There is a redistribution of mass when this occurs. Further, there are the local effects of the depression of the ocean bed and coast at high tide (as this was fairly near new York City), and the change in mass that occurs because of the water. It turns out that these indirect effects very nearly cancel, and the results should be close to the 153 microseconds predicted by direct attraction.

The signal from the pendulum-crystal comparisons show an obvious tidal term when plotted, and when the pendulum clocks were differenced to remove the crystal and compare the pendulum clocks to each other, the regular pattern diminishes significantly, which is a pretty good indication that the effect is on the pendulum clocks alone.

The top graph is the crystal compared to clock 1, and the lower curves show the pendulum clocks compared to each other.

The final result for the three clocks gave results of 128, 147 and 106 microseconds for the shorter duration measurement, and 150, 135 and 127 microseconds for the longer measurement, with errors estimated at between 10 and 20 microseconds. Not a bad result, I think, for some pendulum clocks in the basement, even if it was a millionaire’s basement.